Method and apparatus for mounting photovoltaic modules to shingled surfaces

ABSTRACT

A photovoltaic module for mounting to a roof overlying rafters, wherein the rafters have a given spacing, and wherein the photovoltaic module is to be mounted to the roof with a desired spacing between horizontally-adjacent photovoltaic modules, the photovoltaic module having a width which is a multiple of the given spacing between rafters, after taking into account the desired spacing between horizontally-adjacent photovoltaic modules.

REFERENCE TO PENDING PRIOR PATENT APPLICATION

This patent application claims benefit of pending prior U.S. Provisional Patent Application Ser. No. 61/338,379, filed Feb. 18, 2010 by Zachary A. King et al. for HARDWARE SPECIFICATION FOR MOUNTING PHOTOVOLTAIC MODULES TO SHINGLED SURFACES (Attorney's Docket No. GRRAY-9 PROV), which patent application is hereby incorporated herein by reference.

FIELD OF THE INVENTION

This invention relates to photovoltaic (PV) modules in general, and more particularly to the installation of PV modules on a shingled surface.

DEFINITIONS

For the purposes of this patent application, references to a “north” foot or “north” module shall mean a foot or module that is closer to the peak or higher point of a roof, and references to a “south” foot or “south” module shall mean a foot or module that is closer to the eaves or lower part of a roof. Also, for purposes of this patent application, the term “shingle” shall mean an asphalt roofing shingle, a roof tile shingle and/or any other outer roofing element that is applied to a roof structure in an overlapping manner, and references to a “face” of a shingle shall mean that portion of a shingle that is exposed to the elements and is not covered by another shingle when the shingle is mounted to a roof.

BACKGROUND OF THE INVENTION

Photovoltaic (PV) modules are becoming an increasingly popular means for generating energy as people search for alternative energy sources to supplement and/or replace the combustion of fossil fuels. Some of the benefits of using PV modules in place of fossil fuels include the reduction or elimination of greenhouse gas emissions, protection against the increased price volatility associated with fossil fuels, the partial or complete elimination of dependency on fuel delivery, etc.

A common location for the installation of PV modules is on the roof of a building. There are many benefits to installing PV modules on the roof of a building, e.g., increased direct exposure to sunlight (which can greatly increase the energy-generating capacity of the PV modules), reduced possibility of shadows being cast on the PV modules (which can greatly decrease the energy-generating efficiency of the PV modules), a closer physical proximity between the generating source (the PV modules) and the point of consumption (often within the building itself), etc.

While roofs have been recognized as a generally favorable location for the installation of PV modules, there are some practical considerations associated with installing PV modules on the roof of a building. For example, it is imperative that the PV modules be securely anchored to the roof, but the PV module and its installation on the roof must not detrimentally affect the weather seal of the roof.

Photovoltaic modules are commonly manufactured with mounting elements which are fixed at predetermined locations along the module or which are adjustable within a limited range along the module. The result has been that the dimensions of the module, and the placement of the mounting elements thereon, have to some extent dictated the distance between the mounting elements when they are fixed to the roof or when they are fixed to a support structure which is in turn fixed to the roof (e.g., the rails of a rail-mounted installation such as is discussed below). Such designs have generally failed to take into account any of the structural features of the roof or the orientation of the shingles covering the roof.

Turning now to FIGS. 1 and 2, there is shown a prior art rail-based system for mounting PV modules 5 on a roof 10. The system uses at least two rails 15 which are attached to roof rafters 20 via feet 21 so that rails 15 are generally perpendicular to rafters 20 and parallel to one another. The distance between the rails is to some extent dictated by the location of the mounting elements on the PV modules which are to be attached to the rails. The PV modules are often attached to the rails through the use of an adjustable clamp fitting disposed on the roof-facing side of the module or by some other means disposed on the roof-facing side of the module.

An advantage of the “rail-mounted” approach shown in FIGS. 1 and 2 is that it is relatively easy to ensure that rails 15 are securely attached to the rafters 20 after identifying the location of the rafters, which are typically spaced from one another at standard intervals. By way of example, rails 15 can simply be set on roof 10 so that their feet 21 sit atop rafters 20, and then fasteners are driven through the feet 21, with the fasteners extending through the roof covering (e.g., shingles 25) and into the rafters 20, whereby to secure the rails 15 to the roof. When using this installation method, there is no need to position rails 15 so as to achieve a particular alignment, provided that rails 15 are long enough to cross, and be attached to, a sufficient number of rafters 20 to ensure that the rails are securely fastened to the roof.

There are, however, several drawbacks to the rail-mounted installation approach discussed above. First, if the rails are placed too close to shingles 25, the rails can inhibit proper run-off from the roof. However, raising the height of the rails to facilitate run-off can increase the height of the PV modules and hence increase wind loading on the modules, thereby increasing stress on the roof and the mounting elements.

The use of individual mounting feet to attach each PV module directly to the roof addresses many of the deficiencies associated with a rail-mounted installation system. However, using individual feet to attach PV modules to the roof introduces a new problem, i.e., that of ensuring that each individual foot is appropriately positioned on the roof so that it can be securely fastened to a roof rafter.

Furthermore, additional challenges are presented where the PV modules are to be mounted on a sloped roof covered by shingles, e.g., asphalt shingles, roof tile shingles, etc. For simplicity of description, these issues will hereinafter generally be discussed in the context of asphalt shingles, however, it should be understood these issues are generally equally applicable for all shingles, including roof tile shingles, etc.

Asphalt shingles are a very popular roof covering widely used for residential dwellings. Asphalt shingles are generally manufactured to standard dimensions and installation practices are generally remarkably consistent across the industry. The result is that upon installation, there is a relatively uniform exposed area, or face, for each shingle, and in the case of asphalt shingles, this face is commonly five inches in length (i.e., the dimension that is substantially parallel to the roof rafters) for each shingle.

For PV modules using individual mounting feet, installers are often confronted by the additional problem of the north foot and/or the south foot of the PV module straddling two rows of shingles. This is an unsatisfactory location for a foot, because it prevents the foot from lying flat on the face of a single shingle, thereby undermining secure mounting of the PV module to the roof and/or threatening the weather seal of the roof. Currently, this problem is generally addressed by the installer inserting a shim between the lower shingle and the foot of the PV module so as to provide a flat surface for the foot. Shimming in this fashion, however, is generally undesirable inasmuch as it increases the time necessary to complete the installation, and it makes the area of the foot difficult to flash properly, thereby increasing the likelihood of water being able to penetrate the surface of the roof.

Even in cases where the installer is able to successfully avoid having a foot straddle two shingles at one end of a PV module, the problem will often occur when installing the opposing foot for the other end of the same PV module. This problem is even more likely to occur when installing rows of PV modules, since each successive row of the modules increases the probability of a foot landing on a shingle edge.

The present invention exploits the standard dimensions and installation patterns of shingles, and the standard spacing of roof rafters, and provides a novel method and apparatus for mounting PV modules to shingled surfaces.

SUMMARY OF THE INVENTION

The present invention comprises the provision and use of a novel PV module and its associated mounting elements that allow for a simpler and more effective installation of a single foot-mounted PV module on a roof and/or the installation of an array of foot-mounted PV modules on a roof. The novel PV module and its associated mounting elements ensure that each foot of the PV module, and each foot of each PV module in an array of PV modules, falls on a shingle face, and simultaneously ensure that each foot of the PV module, and each foot of each PV module in an array of PV modules, falls on a roof rafter.

In accordance with the present invention, the PV module and its associated feet are sized so as to have a combined length (i.e., the dimension that is substantially parallel to the roof rafters) that is a multiple of the length of a shingle face, whereby to ensure that each mounting foot falls on a shingle face. Similarly, the PV module is sized so as to have a width (i.e., the dimension that is substantially perpendicular to the roof rafters) that is a multiple of the spacing between the roof rafters, after taking into account the space desired between horizontally-adjacent modules, whereby to ensure that each mounting foot falls on a roof rafter.

Another aspect of the present invention is that each mounting foot for the PV module is sized so that it has a shingle-contacting surface which is smaller than a shingle face so that the mounting foot can rest on a single shingle face when it is fastened to a roof rafter.

The invention also provides for the ability to install the feet of vertically-adjacent modules in a “mated” or “non-mated” fashion. Installing the feet in a “mated” fashion also confers the additional benefit of allowing a single fastener to simultaneously secure multiple feet to a rafter, thereby reducing the number of penetrations that must be made in the roof.

In one preferred form of the invention, there is provided a photovoltaic module for mounting to a roof overlying rafters, wherein the rafters have a given spacing, and wherein the photovoltaic module is to be mounted to the roof with a desired spacing between horizontally-adjacent photovoltaic modules, the photovoltaic module having a width which is a multiple of the given spacing between rafters, after taking into account the desired spacing between horizontally-adjacent photovoltaic modules.

In another preferred form of the invention, there is provided a method for mounting an array of photovoltaic modules to a roof overlying rafters, wherein the rafters have a given spacing, the method comprising:

determining a desired spacing between horizontally-adjacent photovoltaic modules;

providing a plurality of photovoltaic modules each having a width which is a multiple of the given spacing between rafters, after taking into account the desired spacing between horizontally-adjacent photovoltaic modules; and

mounting each photovoltaic module to the roof by securing each photovoltaic module to a rafter underlying the roof, with each photovoltaic module being spaced from a horizontally-adjacent photovoltaic module by the desired spacing.

In another preferred form of the invention, there is provided a photovoltaic module for mounting to a roof overlying rafters, wherein the rafters have a spacing R, and wherein the photovoltaic module is to be mounted to the roof with a spacing H between horizontally-adjacent photovoltaic modules, the photovoltaic module having a width W, wherein:

W=xR−H

and further wherein x is an integer value of 1 or more.

In another preferred form of the invention, there is provided a method for mounting an array of photovoltaic modules to a roof overlying rafters, wherein the rafters have a spacing of R, the method comprising:

determining a desired spacing H between horizontally-adjacent photovoltaic modules;

determining a preferred width W for each photovoltaic module in the array according to the formula:

W=xR−H

where x is an integer value of 1 or more;

providing a plurality of photovoltaic modules of width W; and

mounting each photovoltaic module to the roof by securing each photovoltaic module to a rafter underlying the roof, with each photovoltaic module being spaced from a horizontally-adjacent photovoltaic module by a distance H.

In another preferred form of the invention, there is provided a photovoltaic module for mounting to a roof comprising shingles, wherein each of the shingles has a face of a given length, and wherein the photovoltaic module is to be mounted to the roof with a north foot and a south foot, wherein the north foot has a given effective length and the south foot has a given effective length, the photovoltaic module having a length which, when added to the length of the north foot and the south foot, is a multiple of the given length of a shingle face.

In another preferred form of the invention, there is provided a method for mounting an array of photovoltaic modules to a roof comprising shingles, wherein each of the shingles has a face of a given length, and wherein each of the photovoltaic modules is to be mounted to the roof with a north foot and a south foot, wherein the north foot has a given effective length and the south foot has a given effective length, the method comprising:

providing a plurality of photovoltaic modules each having a length which, when added to the effective length of its associated north foot and associated south foot, is a multiple of the given length of a shingle face; and

mounting each photovoltaic module to the roof by securing the north foot of that photovoltaic module to a single shingle face and securing the south foot of that photovoltaic module to a single shingle face.

In another preferred form of the invention, there is provided a photovoltaic module for mounting to a roof comprising shingles, wherein each of the shingles has a face of length F, and wherein the photovoltaic module is to be mounted to the roof with a north foot having a effective length N′ and a south foot having a effective length S′, the photovoltaic module having a length L, wherein:

L=xF−N′−S′

and further wherein x is an integer value of 1 or more.

In another preferred form of the invention, there is provided a method for mounting an array of photovoltaic modules to a roof comprising shingles, wherein each of the shingles has a face of length F, and wherein each of the photovoltaic modules is to be mounted to the roof with a north foot having a effective length N′ and a south foot having a effective length S′, the method comprising:

providing a plurality of photovoltaic modules of length L, wherein

L=xF−N′−S′

where x is an integer value of 1 or more; and

mounting each photovoltaic module to the roof by securing the north foot of that photovoltaic module to a single shingle face and securing the south foot of that photovoltaic module to a single shingle face.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects and features of the present invention will be more fully disclosed or rendered obvious by the following detailed description of the preferred embodiments of the invention, which is to be considered together with the accompanying drawings wherein like numbers refer to like parts, and further wherein:

FIG. 1 is a partially-transparent perspective view of a prior art rail-mounted PV array, showing two PV modules installed on a sloped roof having shingles and underlying roof rafters;

FIG. 2 is a partially-transparent top view of a prior art rail-mounted PV array, showing two PV modules installed on a sloped roof having shingles and underlying roof rafters;

FIG. 3 is a partially-transparent perspective view of one form of the present invention, showing two PV modules, in a horizontally-adjacent configuration, installed on a sloped roof having shingles and underlying roof rafters;

FIG. 4 is a partially-transparent top view of the PV module array shown in FIG. 3;

FIG. 5 is a perspective view of a north foot;

FIG. 6 is a view of the north mounting edge of a PV module prior to engagement with a north foot;

FIG. 7 is a view of a north mounting edge of the PV module after engagement with a north foot, but prior to rotation of the PV module relative to the north foot;

FIG. 8 is a view of the north mounting edge of a PV module in engagement with a north foot after rotation of the PV module relative to the north foot so that the PV module is in its final mounted position;

FIG. 9 is another view of a north mounting edge of a PV module in engagement with a north foot, with only the north mounting edge of the PV module being shown for clarity of illustration;

FIG. 10 is a view of a south foot;

FIG. 11 is a view of a south foot attached to a south mounting edge of a PV module and about to be attached to a roof;

FIG. 12 is a partially-transparent perspective view of another form of the present invention, showing two PV modules, in a vertically-adjacent configuration, installed on a sloped roof having shingles and underlying roof rafters;

FIG. 13 is a partially-transparent top view of the PV module array shown in FIG. 12;

FIG. 14 is a side view of a north foot and a south foot of vertically-adjacent PV modules, with the two feet being arranged in a mated (e.g., overlapping) configuration;

FIG. 15 is a side view of a north foot and a south foot of vertically-adjacent PV modules, with the two feet being arranged in a non-mated (e.g., abutting) configuration;

FIG. 16 is a partially-transparent perspective view of another form of the present invention, showing four PV modules in both horizontally-adjacent and vertically-adjacent configuration, installed on a sloped roof having shingles and underlying roof rafters; and

FIG. 17 is a partially-transparent top view of the PV module array shown in FIG. 16.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Looking next at FIGS. 3 and 4, there is shown two horizontally-adjacent PV modules 105 secured to a roof 110 in accordance with the present invention. More particularly, PV modules 105 are secured by north feet 112 and south feet 113 to rafters 120 of roof 110, with north feet 112 and south feet 113 engaging the faces of shingles 125. As will hereinafter be discussed, each of the north feet 112 and south feet 113 is positioned so that each foot falls over a rafter 120 to which it is fastened. In addition, as will hereinafter be discussed, the combined length of PV modules 105, north feet 112 and south feet 113 is a multiple of the length of the exposed face of shingles 125 so as to ensure that each foot falls on a shingle face.

Each module 105 is sized such that its width (i.e., as measured perpendicular to the rafters) is a multiple of the distance between rafters 120, after taking into account the space to be provided between adjacent panels, whereby to ensure that each PV module falls over a rafter. In one preferred form of the invention, each PV module is substantially centered on a roof rafter, so that its north foot and south foot are substantially centered across the width of the PV module, whereby to provide a balanced securement of the PV module to the roof.

Each module 105 and its associated feet 112, 113 are sized such that their combined vertical length (i.e., as measured parallel to the rafters) is a multiple of the length of the exposed face of the shingles 125 (FIGS. 12 and 13) so as to ensure that each foot falls flat on the face of a shingle. As will hereinafter be discussed, the dimensions of each module 105 and its associated feet 112, 113 are sized so as to ensure this result regardless of whether the feet of the vertically-adjacent modules are arranged in an overlapping (mated) or abutting (non-mated) configuration, as will hereinafter be discussed.

Installation of the PV modules 105 and feet 112, 113 is relatively straightforward. Looking now at FIG. 5, there is shown a perspective view of a north foot 112. North foot 112 is placed flat on the face of a single shingle and fastened to a roof rafter 120 by means of appropriate hardware, e.g., a 5/16 inch lag bolt which is inserted through hole 130 in north foot 112. Photovoltaic module 105 is then “hung” from north foot 112, as shown in FIGS. 6-9, by inserting a portion of the north mounting edge 135 of PV module 105 into the hook portion 140 of the north foot 112. Preferably the PV module is substantially centered (widthwise) on north foot 112 when it is hung on the north foot. After the PV module 105 is hung from north foot 112, and looking now at FIGS. 10 and 11, south foot 113 may be slidingly attached to the south mounting edge 145 of PV module 105 with screws 150 which extend through holes 151 in south foot 113 and into south mounting edge 145. After south foot 113 is slidingly attached to PV module 105, south foot 113 is slid along south mounting edge 145 until it is directly over a roof rafter 120, which action will preferably also substantially center (widthwise) south foot 113 on the PV module, at which point south foot 113 can be fixed in place with respect to PV module 105 by tightening screws 150. PV module 105 may then be secured to the roof by passing a bolt through hole 155 in south foot 113 and into the underlying rafter 120. As noted above, by appropriately sizing the length of PV module 105 and its associated feet 112, 113, it can be ensured that south foot 113 will always sit on the face of a shingle by virtue of the fact that the previously-installed north foot 112 of the same module sits on the face of a shingle.

Looking next at FIGS. 12 and 13, there is shown two vertically-adjacent PV modules 105 secured to roof rafters 120 of a sloped roof covered with shingles 125. Each of the north foot 112 and south foot 113 is positioned so that it will fall over a rafter 120 to which it can be fastened. Preferably the PV module is substantially centered (widthwise) on north foot 112 and south foot 113. Furthermore, in accordance with the present invention, each of the feet falls on a single shingle 125.

More particularly, in accordance with the present invention, PV module 105, north foot 112 and south foot 113 are collectively sized such that when two modules are installed in vertically-adjacent positions to one another, the feet are spaced at distances that are multiples of the length of the shingle face, and therefore, each north foot 112 and south foot 113 can fall on a shingle. In other words, if the north foot 112 of a PV module falls on a shingle face, then the south foot 113 of that same PV module will also fall on a shingle face.

Furthermore, where the PV module is part of an array of PV modules having vertically-adjacent PV modules, by appropriately sizing PV modules 105, north feet 112 and south feet 113, positioning the north foot of one PV module on a shingle face will automatically ensure that the other feet of the PV modules of that array will also fall on a shingle face.

Significantly, when PV modules 105 are installed in such a vertically-adjacent configuration, the invention provides for flexibility with respect to the particular disposition (e.g., mated or overlapping versus non-mated or abutting) of the south foot 113 of the north PV module and the north foot 112 of the south PV module, even while ensuring that each foot falls on a shingle face.

More particularly, and looking now at FIGS. 12-14, in one form of the invention, south foot 113 of the north module and north foot 112 of the south module are attached to roof rafter 120 in a mated (i.e., overlapping) configuration. This configuration allows both feet to be secured to rafter 120 with a single fastener, e.g., a lag bolt, resulting in only one penetration of the roof to attach both feet to the rafter rather than one penetration of the roof for each foot. To facilitate this mated fit, south foot 113 is sized so that it may be placed on top of the north foot 112, and the holes 155, 130 are disposed on their respective feet such that when the south foot is placed on top of the north foot in the mated (i.e., overlapping) configuration, the holes in each will align. This aspect of the present invention allows the installer to fix the overlapping north and south feet of the two modules to the roof rafter with a single fastener. By appropriately sizing the lengths of PV module 105, north foot 112 and south foot 113, each of the feet will land on the face of a shingle.

Notwithstanding the foregoing, the lengths of PV module 105, north foot 112 and south foot 113 may also be sized such that the feet may be installed in an abutting, non-mated configuration, as shown in FIG. 15. Again, the respective lengths of PV module 105, north foot 112 and south foot 113 are such that each of the feet can land on the face of a shingle.

Looking last at FIGS. 16 and 17, four modules 105 are installed on a sloped roof in a manner contemplated by the present invention. Each of the feet falls on a single shingle 125 and over a rafter 120 (the abutting north feet 112 and south feet 113 are shown in mated configuration), and each module 105 is centered over a rafter 120.

In general, it is believed that where a roof has a rafter spacing of R, and where it is desired to have a spacing of H between horizonally-adjacment modules, each module may advantageously have a width W such that:

W+H=xR

or

W=xR−H

where x is an integer value of 1 or more.

In general, it is believed that, where the roof has shingles of face length F, the north foot has a length of N and the south foot has a length of S, and where the module is not intended to be part of an array of PV modules, each module may advantageously have a length L such that

L+N+S=xF

or

L=xF−N−S

where x is an integer of value 1 or more.

In general, it is believed that where the roof has shingles of face length F, the north foot has a length of N and the south foot has a length of S, and where the module is intended to be part of an array of vertically-adjacent PV modules where the feet are arranged in an abutting configuration with no gap between the south foot of the north module and the north foot of the south module, then each module may advantageously have a length L such that

L+N+S=xF

or

L=xF−N−S

where x is an integer of value 1 or more.

In general, it is believed that where the roof has shingles of face length F, the north foot has a length of N and the south foot has a length of S, and where the module is intended to be part of an array of vertically-adjacent PV modules where the feet are arranged in an abutting configuration with a uniform gap G between the south foot of the north module and the north foot of the south module, then each module may advantageously have a length L such that

L+N+S+G=xF

or

L=xF−N−S−G

where x is an integer of value 1 or more.

In general, it is believed that where the roof has shingles of face length F, the north foot has a length of N and the south foot has a length of S, and where the module is intended to be part of an array of vertically-adjacent PV modules where the feet are arranged in a mated (i.e., overlapped) configuration, then each module may advantageously have a length L such that

L+aN+bS=xF

or

L=xF−aN−bS

where x is an integer of value 1 or more, a+b=1 and neither a nor b is zero.

Furthermore, it will be appreciated that in the case of vertically-adjacent PV modules, the “effective length” of the north foot plus the “effective length” of the south foot is equal to the vertical gap between vertically-adjacent PV modules.

Thus, in general, it is believed that where the module is intended to be part of an array of vertically-adjacent PV modules where the feet may be arranged in a mated (i.e., overlapped) or non-mated (i.e., abutting, with or without a gap therebetween) configuration, and where the roof has shingles of face length F, the north foot has an effective length of N′ and the south foot has an effective length of S′ (where the terms “effective length” reflect whether the feet are arranged in an overlapped or abutting configuration, where the abutting configuration may or may not have a gap therebetween), then each module may advantageously have a length L such that

L=xF−N′−S′

where x is an integer of value 1 or more.

Example

In one preferred form of the invention, where the spacing between rafters 120 is 16 inches on-center, and where the length of the face of a shingle is 5 inches, and where it is desired to provide an array of PV modules having a gap of 0.5 inches between horizontally-adjacent PV modules and the feet of vertically-adjacent PV modules are mated (i.e., overlapping), the PV module 105 may have a length of 62.75 inches, a width of 31.5 inches, north foot 112 may have an effective length of 1.25 inches and south foot 113 may have an effective length of 1.0 inches, whereby to ensure that all feet will fall on a rafter and flat on a shingle, where a north foot 112 is placed above a rafter and appropriately placed on the face of a shingle.

MODIFICATIONS OF THE PREFERRED EMBODIMENTS

It should be understood that many additional changes in the details, materials, steps and arrangements of parts, which have been herein described and illustrated in order to explain the nature of the present invention, may be made by those skilled in the art while still remaining within the principles and scope of the invention. 

1. A photovoltaic module for mounting to a roof overlying rafters, wherein the rafters have a given spacing, and wherein the photovoltaic module is to be mounted to the roof with a desired spacing between horizontally-adjacent photovoltaic modules, the photovoltaic module having a width which is a multiple of the given spacing between rafters, after taking into account the desired spacing between horizontally-adjacent photovoltaic modules.
 2. A method for mounting an array of photovoltaic modules to a roof overlying rafters, wherein the rafters have a given spacing, the method comprising: determining a desired spacing between horizontally-adjacent photovoltaic modules; providing a plurality of photovoltaic modules each having a width which is a multiple of the given spacing between rafters, after taking into account the desired spacing between horizontally-adjacent photovoltaic modules; and mounting each photovoltaic module to the roof by securing each photovoltaic module to a rafter underlying the roof, with each photovoltaic module being spaced from a horizontally-adjacent photovoltaic module by the desired spacing.
 3. A photovoltaic module for mounting to a roof overlying rafters, wherein the rafters have a spacing R, and wherein the photovoltaic module is to be mounted to the roof with a spacing H between horizontally-adjacent photovoltaic modules, the photovoltaic module having a width W, wherein: W=xR−H and further wherein x is an integer value of 1 or more.
 4. A method for mounting an array of photovoltaic modules to a roof overlying rafters, wherein the rafters have a spacing of R, the method comprising: determining a desired spacing H between horizontally-adjacent photovoltaic modules; determining a preferred width W for each photovoltaic module in the array according to the formula: W=xR−H where x is an integer value of 1 or more; providing a plurality of photovoltaic modules of width W; and mounting each photovoltaic module to the roof by securing each photovoltaic module to a rafter underlying the roof, with each photovoltaic module being spaced from a horizontally-adjacent photovoltaic module by a distance H.
 5. A photovoltaic module for mounting to a roof comprising shingles, wherein each of the shingles has a face of a given length, and wherein the photovoltaic module is to be mounted to the roof with a north foot and a south foot, wherein the north foot has a given effective length and the south foot has a given effective length, the photovoltaic module having a length which, when added to the length of the north foot and the south foot, is a multiple of the given length of a shingle face.
 6. A method for mounting an array of photovoltaic modules to a roof comprising shingles, wherein each of the shingles has a face of a given length, and wherein each of the photovoltaic modules is to be mounted to the roof with a north foot and a south foot, wherein the north foot has a given effective length and the south foot has a given effective length, the method comprising: providing a plurality of photovoltaic modules each having a length which, when added to the effective length of its associated north foot and associated south foot, is a multiple of the given length of a shingle face; and mounting each photovoltaic module to the roof by securing the north foot of that photovoltaic module to a single shingle face and securing the south foot of that photovoltaic module to a single shingle face.
 7. A photovoltaic module for mounting to a roof comprising shingles, wherein each of the shingles has a face of length F, and wherein the photovoltaic module is to be mounted to the roof with a north foot having a effective length N′ and a south foot having a effective length S′, the photovoltaic module having a length L, wherein: L=xF−N′−S′ and further wherein x is an integer value of 1 or more.
 8. A method for mounting an array of photovoltaic modules to a roof comprising shingles, wherein each of the shingles has a face of length F, and wherein each of the photovoltaic modules is to be mounted to the roof with a north foot having a effective length N′ and a south foot having a effective length S′, the method comprising: providing a plurality of photovoltaic modules of length L, wherein L=xF−N′−S′ where x is an integer value of 1 or more; and mounting each photovoltaic module to the roof by securing the north foot of that photovoltaic module to a single shingle face and securing the south foot of that photovoltaic module to a single shingle face. 